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Equation of common tangent touching the circle (x-3) 2 +y 2 =9 and parabola y 2 =4x above the x-axis is
Center of circle: (3,0)Equation of tangent on parabola:y=mx+a/ma=1y=mx+1/mPerpendicular Distance from the center of the circle = 3|3m+1/m|/(1+m)1/2=3m2=1/3 => m=+1/√3 or -1/√3As tangent is above x-axis, slope is (+)veTherefore, Equation of tangent:y=x/√3+√3=> √3y=x+3
Center of circle: (3,0)
Equation of tangent on parabola:
y=mx+a/m
a=1
y=mx+1/m
Perpendicular Distance from the center of the circle = 3
|3m+1/m|/(1+m)1/2=3
m2=1/3 => m=+1/√3 or -1/√3
As tangent is above x-axis, slope is (+)ve
Therefore, Equation of tangent:
y=x/√3+√3=> √3y=x+3
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